# Demographics, Investment, and Capital Deepening: How Aging Reshapes Production Structure

## Abstract

This paper investigates how demographic change drives investment effort, capital deepening, and production structure across a panel of up to 175 countries from 1970 to 2024. Using the three-component demographic structure vector $Z = (Z_1, Z_2, Z_3)$ from Higgins (1998), we test whether aging societies invest more intensively and how this relates to their trade and current account positions. We distinguish four automation proxies: investment-to-GDP (I/Y), the capital-output ratio (K/Y), capital per worker (K/L), and labor productivity. Demographics robustly predict I/Y ($Z_1 = 32.3$, $p < 0.01$) and K/L ($Z_1 = 0.10$, $p < 0.05$), but the true capital-output ratio K/Y is marginally negative ($Z_1 = -5.1$, $p < 0.10$), indicating that demographics drive investment effort rather than the accumulated capital intensity of the production structure. The I/Y effect is concentrated in non-OECD economies ($Z_1 = 37.0$, $p < 0.05$) and declines monotonically with income. In the OECD, I/Y acts as a suppressor variable in the current account regression: controlling for it reveals two opposing demographic channels — a surplus-generating investment channel and a deficit-generating consumption channel — that cancel in the baseline ($-599\%$ attenuation in the full sample, $140\%$ in the OECD). By contrast, controlling for K/Y or K/L barely moves the demographic coefficient (attenuation $< 25\%$), confirming that the suppression is specific to investment effort. $Z \times KAOPEN$ interactions on I/Y are statistically insignificant in the full sample, though they remain significant for K/L in the OECD, indicating that the capital account openness channel is OECD-specific. Within the eurozone, I/Y mediates 98% of the amplified demographic effect on the current account. Demographics are associated with trade openness ($Z_1 = 95.1$, $p < 0.05$), but the demographic distance measure is statistically insignificant, limiting claims about demographic comparative advantage. Results are robust to 5-year lags, first differences, and exclusion of financial centers.

## 1. Introduction

Population aging is among the most consequential structural transformations facing the global economy. As dependency ratios shift and working-age populations shrink, firms face powerful incentives to substitute capital for increasingly scarce labor. Acemoglu and Restrepo (2017, 2022) formalize this intuition, showing that aging economies adopt automation technologies at higher rates, partially offsetting the negative growth effects of labor force decline. Yet the macroeconomic implications of this automation response for capital flows, trade patterns, and comparative advantage remain underexplored.

This paper bridges the demographics-capital flows literature with the automation and capital deepening literatures. Our core hypothesis is that aging generates higher investment effort, which interacts with the well-documented relationship between demographic structure and the current account. We distinguish carefully between investment effort (I/Y), the capital-output ratio (K/Y), capital per worker (K/L), and labor productivity — proxies that measure different aspects of the production structure and respond differently to demographic pressures.

We organize the analysis around four questions. First, do demographics predict investment and capital deepening proxies in a panel setting? Second, does investment effort mediate — or suppress — the demographic channel to the current account? Third, is there evidence that demographic heterogeneity across countries is associated with trade patterns? Fourth, do capital account openness and income level moderate these relationships?

Our contribution is threefold. We provide the first systematic panel evidence linking demographic structure to multiple capital deepening proxies using the Higgins Z vector, which captures the full age-distribution shape rather than simple dependency ratios. We test the Acemoglu-Restrepo mechanism in an international panel context, finding that demographics drive investment effort (I/Y) but not the capital-output ratio (K/Y), a distinction with important implications for the automation hypothesis. And we document that investment effort acts as a suppressor variable in the demographic-CA relationship, revealing offsetting channels that cancel in the baseline.

## 2. Literature Review

### 2.1 Demographics and Automation

Acemoglu and Restrepo (2017) document that countries experiencing more rapid aging have adopted more industrial robots per worker, interpreting this as directed technological change toward automation. Their 2022 paper extends the framework to show that automation can fully offset the negative growth effects of demographic decline in advanced economies. Abeliansky and Prettner (2023) confirm the cross-country pattern using broader automation measures and find that the effect is concentrated in manufacturing.

The lifecycle savings hypothesis (Modigliani-Brumberg) predicts that aging societies accumulate capital, driving down the marginal product and generating capital outflows. The automation channel adds nuance: capital deepening in aging economies is not merely passive accumulation but reflects active substitution of machines for workers. This distinction matters for whether demographic capital flows are temporary (lifecycle) or permanent (structural comparative advantage).

### 2.2 Trade Openness and Demographic Structure

The trade literature has largely ignored demographics as a determinant of trade openness and production network position. Baldwin (2016) emphasizes trade costs, technology diffusion, and institutional quality as drivers of GVC participation. Yet demographic structure plausibly affects trade patterns through multiple channels: labor costs (young populations with large labor forces attract labor-intensive segments), capital availability (older populations generate savings that fund capital-intensive production), and market size for specific product categories.

Cravino, Levchenko, and Rojas (2022) show that trade amplifies the welfare effects of demographic change by allowing specialization according to comparative advantage. We test whether demographics are associated with trade openness, though we note at the outset that trade openness is a coarse proxy for comparative advantage and GVC position.

### 2.3 Capital Flows and Production Structure

The Higgins (1998) demographic structure vector $Z = (Z_1, Z_2, Z_3)$ captures the net lifecycle savings position of a population's age distribution. Previous work in this project confirms that $Z_1$ robustly predicts the current account, with coefficient magnitudes around 40-50 basis points and significance at the 1% level across specifications. The capital deepening paper (companion) shows that demographics predict investment-to-GDP ratios but not TFP, suggesting a capital-quantity rather than capital-quality channel.

This paper asks whether investment effort and capital deepening represent mechanisms through which demographic structure transmits to the current account. We test this by examining whether controlling for investment-to-GDP (I/Y) or the capital-output ratio (K/Y) attenuates or amplifies the demographic coefficient in the CA regression, distinguishing mediation from suppression.

## 3. Data and Methodology

### 3.1 Data

Our panel covers up to 175 countries from 1970 to 2024 (237 in the underlying dataset, with regression samples ranging from 127 to 189 countries depending on variable coverage), constructed from multiple sources. Demographic variables ($Z_1, Z_2, Z_3$, old-age dependency ratio, youth dependency ratio, working-age share) are computed from UN World Population Prospects age distributions using the Higgins (1998) methodology. Current account data, GDP per capita (PPP), trade openness, gross investment share, and fiscal variables are from the World Development Indicators and IMF World Economic Outlook. Capital account openness (KAOPEN) is from Chinn-Ito. Net foreign asset positions are from the updated Lane-Milesi-Ferretti dataset.

We construct four automation and capital deepening proxies, each measuring a distinct aspect of the production structure. (i) Investment-to-GDP (I/Y): gross capital formation as a share of GDP (WDI series NE.GDI.TOTL.ZS). This measures investment *effort* — the flow of resources directed toward capital accumulation in a given year. Because the WDI measure includes inventory changes, 9 country-year observations (Djibouti, Iraq, Sierra Leone, Azerbaijan — all conflict or collapse years) report negative values; we retain these rather than censoring, but results are unchanged if they are dropped. (ii) Capital-output ratio (K/Y): the ratio of the real capital stock (rnna) to real output (rgdpo), both at constant 2017 national prices, from PWT 10.01. This measures the accumulated capital intensity of the production structure. (iii) Capital per worker (K/L): the real capital stock divided by total employment, from PWT. (iv) Labor productivity: GDP per capita at PPP, from WDI. We also use the labor share of income (labsh) from PWT and trade openness (exports plus imports as a share of GDP) as an exploratory trade measure. Financial centers (Luxembourg, Ireland, Hong Kong, Singapore, Switzerland, Netherlands, Belgium) are flagged for robustness exclusion. In earlier drafts, "capital intensity" referred to I/Y; we now use explicit labels throughout to avoid ambiguity between investment effort (a flow measure) and capital-output ratios (a stock measure).

### 3.2 Empirical Strategy

Our baseline specification is:

$$
Y_{it} = \alpha_i + \delta_t + \beta_1 Z_{1,it} + \beta_2 Z_{2,it} + \beta_3 Z_{3,it} + \gamma' X_{it} + \varepsilon_{it}
$$

where $Y_{it}$ is the capital deepening proxy (I/Y, K/Y, K/L, or labor productivity) for country $i$ in year $t$; $\alpha_i$ and $\delta_t$ are country and year fixed effects; $Z_{1}, Z_{2}, Z_{3}$ are the Higgins demographic components; and $X_{it}$ includes controls for fiscal balance, lagged NFA position, GDP growth, and capital account openness. We estimate by Panel GLS with Prais-Winsten correction for AR(1) serial correlation.

To test KAOPEN moderation, we estimate:

$$
Y_{it} = \alpha_i + \delta_t + \beta' Z_{it} + \phi' (Z_{it} \times KAOPEN_{it}) + \gamma' X_{it} + \varepsilon_{it}
$$

For mediation/suppression analysis, we compare the $Z$ coefficients with and without controlling for each proxy, following Baron and Kenny (1986). If a proxy mediates the demographic channel, the $Z$ coefficients on the current account should attenuate (0–100%). If the $Z$ coefficient instead amplifies or changes sign, the proxy acts as a suppressor — revealing opposing channels that cancel in the baseline.

Income tercile heterogeneity is assessed by splitting the sample into low, middle, and high GDP per capita groups using within-sample tercile cutoffs. OECD/non-OECD splits provide an alternative grouping that captures institutional and development-stage differences.

A note on model fit: several specifications report negative $R^2$ values. This arises under GLS estimation when the model's fit, after Prais-Winsten AR(1) correction and within-group demeaning, is worse than a simple within-group mean. Coefficient estimates and standard errors remain valid; only the goodness-of-fit measure is uninterpretable as variance explained.

## 4. Results

### 4.1 Demographics and Capital Deepening Proxies

Table A1 presents the corrected baseline results for demographics predicting all four proxies. The results reveal an important distinction between investment effort and accumulated capital intensity.

**Investment-to-GDP (I/Y)**: $Z_1$ enters strongly positive ($\beta = 32.3$, $p < 0.01$), confirming that populations with net positive lifecycle savings positions invest a larger share of output. The effect is concentrated in non-OECD economies ($Z_1 = 37.0$, $p < 0.05$); in the OECD subsample, $Z_1$ is positive but insignificant ($26.5$, NS).

**Capital-output ratio (K/Y)**: $Z_1$ is marginally negative ($\beta = -5.1$, $p < 0.10$). Demographics weakly predict *lower* accumulated capital intensity, the opposite direction from the automation hypothesis. This finding reinforces the distinction between investment effort and automation: aging societies invest more as a share of GDP, but this does not translate into a higher capital-to-output ratio — if anything, K/Y is marginally lower. An accounting identity clarifies why. The capital-output ratio evolves as $\Delta(K/Y) \approx I/Y - (\delta + g_Y) \cdot K/Y$, where $\delta$ is the depreciation rate and $g_Y$ is output growth. K/Y rises only when gross investment exceeds the sum of depreciation and output-driven dilution. If aging raises I/Y but simultaneously raises depreciation (older capital stocks require more replacement investment), shifts output composition toward services (raising $g_Y$ in sectors with low capital requirements), or redirects investment toward intangible capital not captured in PWT's rnna measure, K/Y can remain flat even as I/Y rises. The I/Y–K/Y disconnect is therefore not puzzling but structurally expected when gross investment serves maintenance and replacement rather than net deepening.

**Capital per worker (K/L)**: $Z_1$ is positive in the full sample ($0.10$, $p < 0.05$) but negative in the OECD ($-0.41$, $p < 0.01$) — a sign reversal that merits explanation. In the OECD, aging societies have *less* capital per worker. Several mechanisms are consistent with this pattern. First, immigration and rising female labor force participation in aging OECD economies expand the denominator (L) faster than capital accumulates, a labor dilution effect documented in the companion capital deepening paper. Second, OECD economies have shifted toward services, where capital per worker is lower than in manufacturing; this compositional shift correlates with aging. Third, depreciation and obsolescence of older capital stocks may offset gross investment, so that net capital growth lags employment growth. Fourth, intangible capital (software, R&D, organizational capital) is not captured in PWT's rnna measure, potentially understating capital in aging knowledge economies. The sign reversal is therefore not model instability but a genuine feature of how capital and labor evolve differently across development stages.

**Labor productivity**: $Z_1$ is insignificant in the full sample after controlling for fiscal balance, NFA, growth, and KAOPEN.

The age decomposition (Table 3) reveals that both old-age and youth dependency ratios are negatively associated with I/Y ($-28.5$ and $-15.6$, respectively, both $p < 0.01$), indicating that a larger working-age share — not aging per se — drives investment effort. This is consistent with a demographic dividend interpretation rather than the Acemoglu-Restrepo automation hypothesis. The working-age share control absorbs some of the $Z$ effect on labor productivity, suggesting that the labor supply channel partially explains the correlation.

### 4.2 Investment Effort and the Current Account: Suppression, Not Mediation

Table A2 tests whether each proxy mediates or suppresses the $Z \to CA$ relationship. The results differ sharply across proxies, clarifying the mechanism.

**I/Y (investment effort)** acts as a strong suppressor. In the full sample, $Z_1$ enters the baseline CA regression at 7.0 (NS, $p = 0.59$). When I/Y is added, $Z_1$ *increases* to 49.2 ($p < 0.001$) — a dramatic amplification with $-599\%$ attenuation. I/Y itself enters negatively ($-0.68$, $p < 0.001$): higher investment shares are associated with current account deficits, and controlling for this deficit-generating channel reveals the underlying surplus-generating demographic effect. In the OECD, the suppression is even more dramatic: $Z_1$ flips from $-42.0$ (NS) to $+16.6$ (NS), producing $140\%$ attenuation — a classic suppression pattern revealing two opposing channels. Aging OECD economies simultaneously generate current account surpluses through investment (the capital deepening channel) and deficits through a residual channel, likely pension and healthcare consumption.

**K/Y (capital-output ratio)** has no mediating or suppressing effect. Controlling for K/Y barely moves $Z_1$ (attenuation $-0.4\%$ in full sample, $-0.1\%$ in OECD). Since demographics only weakly predict K/Y (Section 4.1), this near-zero mediation is expected.

**K/L (capital per worker)** shows modest mediation in the full sample ($24.1\%$ attenuation) but negligible in the OECD ($2.0\%$ attenuation).

The contrast is informative. The suppression result is specific to I/Y — the flow of new investment — rather than the stock of capital. This means the offsetting channels in the demographic-CA relationship operate through how much societies invest each year, not through how much capital they have accumulated. The K/Y result (marginally negative) rules out a strict "automation" interpretation: demographics do not predict higher capital intensity of the production structure, only the investment share of output.

### 4.3 Demographics and Trade Openness

Table 5 reports exploratory regressions of trade openness on demographic structure. $Z_1$ enters positively ($95.1$, $p < 0.05$), but the sign reverses in the OECD ($-275.0$, $p < 0.01$) while strengthening in non-OECD economies ($156.5$, $p < 0.01$). The relationship is not stable across subsamples.

Table 6 tests the demographic distance hypothesis. Countries whose demographic structure deviates more from the global mean do *not* exhibit significantly greater trade openness: the demographic distance coefficient is statistically insignificant across all specifications ($p > 0.10$). This null result limits claims about demographic comparative advantage. While demographic structure correlates with trade openness through the $Z$ vector, this likely reflects development-stage correlates (younger, more open economies) rather than a Heckscher-Ohlin mechanism driven by demographic dissimilarity.

We retain these results as exploratory evidence that demographics are associated with trade patterns, but we do not interpret them as evidence for demographic comparative advantage. Trade openness is a coarse proxy, and the absence of a demographic distance effect suggests that the $Z$-trade correlation operates through other channels (e.g., development level, institutional quality) rather than factor endowment heterogeneity.

### 4.4 KAOPEN and Income Interactions

Table 8 presents the KAOPEN interaction results. $Z \times KAOPEN$ interactions are statistically insignificant for I/Y ($Z_1 \times KAOPEN = -4.9$, $p > 0.10$; $Z_2 \times KAOPEN = 0.7$, NS; $Z_3 \times KAOPEN = -0.03$, NS) and for labor productivity (all $p > 0.10$). Capital account openness does not modulate how demographics translate into investment effort or labor productivity outcomes in the expanded panel. The one exception is capital per worker (K/L), where $Z_1 \times KAOPEN = 0.035$ ($p < 0.05$), suggesting that openness modulates the capital-labor ratio channel.

The OECD/non-OECD split reveals that the K/L interaction is exclusively an OECD phenomenon. In OECD economies, all three $Z \times KAOPEN$ interactions on K/L are significant ($Z_1 \times KAOPEN = -0.21$, $p < 0.01$; $Z_2 = 0.027$, $p < 0.01$; $Z_3 = -0.0009$, $p < 0.05$), while in non-OECD economies all are insignificant. For I/Y, KAOPEN interactions are insignificant in both OECD and non-OECD subsamples. The collapse of KAOPEN interactions on I/Y in the expanded 140-country panel — compared to the 69-country panel where they were significant — indicates that the openness-investment channel is not a universal phenomenon but was driven by OECD composition in the smaller sample.

Table A3 reports income tercile heterogeneity with all four proxies, revealing that different proxies show different income patterns:

**I/Y**: The demographic effect declines monotonically with income — low-income ($Z_1 = 65.4$, $p < 0.10$), middle-income ($36.6$, NS), high-income ($16.2$, NS). Demographic pressures most readily translate into investment effort in economies with the largest investment gaps.

**K/Y**: The pattern reverses. Low-income economies show a positive effect ($Z_1 = 19.5$, $p < 0.05$), middle-income show a significant negative effect ($-12.7$, $p < 0.01$), and high-income show null ($-1.9$, NS). This is consistent with capital-output ratios being driven by development stage rather than demographics in richer economies.

**K/L**: Low-income positive ($0.11$, $p < 0.01$), middle-income strongly negative ($-0.15$, $p < 0.01$), high-income null ($-0.03$, NS). The middle-income sign reversal likely reflects labor force dynamics — middle-income economies in demographic transition experience rapid employment growth that dilutes capital per worker.

The absence of a uniform "middle-income peak" across proxies undermines a simple absorptive capacity interpretation. Instead, the pattern is consistent with demographics operating through different channels at different development stages: investment effort in low-income economies, capital deepening in early-stage economies, and labor market dynamics in middle-income transitions.

### 4.5 Regime-Contingent I/Y Suppression

The trilemma paper documents that eurozone membership amplifies the demographic effect on the current account, with $Z_1$ coefficients an order of magnitude larger within the eurozone than for floating OECD economies. Table 14 tests whether I/Y mediates or suppresses this amplified effect differently across exchange rate regimes.

Within the eurozone (post-adoption, 411 observations), $Z_1$ enters the baseline CA regression at $-132.3$ ($p < 0.01$), consistent with the trilemma paper's finding of $-214$ on its larger panel. Adding I/Y attenuates this to $-3.1$ (NS, $p = 0.95$), a 97.7% reduction — near-complete mediation. For OECD floaters, the baseline $Z_1$ is $-11.8$ (NS, $p = 0.72$), attenuating to $+44.5$ (NS, $p = 0.16$) — a 476% shift that mirrors the full-OECD suppression pattern. In both subsamples, I/Y enters with a large negative coefficient ($-0.93$ to $-0.99$, $p < 0.001$), confirming that higher investment-to-GDP ratios are associated with current account deficits after controlling for demographics.

The key finding is that I/Y mediates nearly all of the demographic effect within the eurozone (98%) compared to floaters, where 476% attenuation indicates full suppression with sign reversal. This is consistent with the logic that eurozone members cannot adjust the nominal exchange rate to offset investment-driven competitiveness shifts, so the I/Y channel operates more forcefully on the current account. Eurozone and floater regressions use the trilemma-consistent three-control specification (fiscal balance, lagged NFA, GDP growth) to maximize sample coverage and ensure comparability across papers.

Splitting the eurozone into core (Germany, Netherlands, Austria, Finland, Belgium) and periphery (Italy, Spain, Portugal, Greece, Ireland) reveals an asymmetry in the investment channel (Table 16). The core exhibits 242% attenuation — a strong suppression pattern where I/Y flips the demographic coefficient from $-15.2$ to $+21.5$ — while the periphery shows 82% mediation ($-265.8$ to $-47.9$). The periphery's large baseline ($Z_1 = -265.8$, $p < 0.05$) indicates that aging drives substantial current account deficits in the southern eurozone, and I/Y mediates roughly four-fifths of this effect. The first-stage relationship ($Z \to I/Y$) is imprecise in both subsamples: core ($Z_1 = 64.5$, NS) and periphery ($Z_1 = 76.2$, NS), with the periphery showing a larger point estimate than the core — the opposite of expectations. Both subsamples are small (130 and 128 observations respectively), so individual coefficients are imprecise, but the pattern of stronger mediation in the periphery (82%) versus suppression in the core (242%) is consistent with the core's dual-channel structure.

### 4.6 Robustness

Table 10 shows that 5-year lagged demographics strengthen the I/Y result ($Z_{1,t-5} = 34.9$, $p < 0.01$, vs. contemporary $32.3$) and render labor productivity significant ($Z_{1,t-5} = 16{,}630$, $p < 0.05$, vs. contemporary $8{,}075$, NS). For K/L, lags weaken the result ($-0.03$, NS), suggesting that the K/L relationship is more contemporaneous. The lagged specification also mitigates reverse causality concerns, as it is implausible that current automation outcomes cause past demographic structure.

Table 11 presents first-differenced regressions. For I/Y, $\Delta Z_1$ remains significant ($43.6$, $p < 0.05$), indicating that demographic changes predict investment changes even in differences. For K/L, first differences are insignificant, consistent with the level-effect nature of the capital-labor relationship. The mixed first-difference results suggest that I/Y responds more quickly to demographic shifts than the stock measures K/Y and K/L.

Table 12 confirms robustness across subsamples. Excluding financial centers (Luxembourg, Ireland, Hong Kong, Singapore, Switzerland, Netherlands, Belgium) does not materially change the results, indicating that the findings are not driven by outlier economies with atypical investment-to-GDP ratios. The non-OECD subsample shows stronger I/Y effects, while the OECD shows the suppression pattern most clearly in mediation analysis.

## 5. Discussion

Our findings connect several literatures, but with important qualifications that differ from the original hypothesis.

**Investment effort, not automation.** The central finding is that demographics predict I/Y (investment effort) but K/Y (the capital-output ratio) is marginally negative. This distinction matters for the Acemoglu-Restrepo interpretation. If aging drove automation — the substitution of capital for labor in production — we would expect K/Y and K/L to respond positively to demographic maturity. Instead, K/Y is marginally negative ($p < 0.10$) and K/L is negative in the OECD. The demographic channel operates through how much societies invest each year, not through the capital intensity of their production structure. This is more consistent with lifecycle savings (Modigliani-Brumberg) and investment-home-bias interpretations than with directed technological change.

**Suppression, not mediation.** I/Y acts as a suppressor variable in the CA regression, not a mediator. Controlling for I/Y amplifies the demographic coefficient from 7.0 (NS) to 49.2 ($p < 0.001$) in the full sample — a dramatic $-599\%$ attenuation — and flips its sign in the OECD ($-42.0$ to $+16.6$, $140\%$ attenuation). This reveals two opposing channels: demographics generate current account surpluses through investment (aging societies invest less, freeing resources for export) and current account deficits through consumption (pension and healthcare spending raises imports). These channels largely cancel in the baseline, and I/Y control separates them. K/Y attenuation is near zero ($-0.4\%$ full, $-0.1\%$ OECD) and K/L shows only modest mediation ($24\%$ full, $2\%$ OECD), confirming the suppression effect is specific to investment effort.

**Trade openness, not comparative advantage.** Demographics are associated with trade openness through the $Z$ vector ($Z_1 = 95.1$, $p < 0.05$), but the demographic distance measure is insignificant. We cannot claim that demographically dissimilar countries trade more in a Heckscher-Ohlin sense. The $Z$-trade correlation likely reflects development-stage correlates rather than factor endowment heterogeneity.

**KAOPEN interactions are OECD-specific.** In the expanded 140-country panel, $Z \times KAOPEN$ interactions on I/Y and labor productivity are statistically insignificant — a major revision from the 69-country panel where they appeared significant. The one exception is capital per worker (K/L), where KAOPEN interactions are significant in the OECD but null in non-OECD economies. This suggests that capital account openness modulates the capital-labor substitution channel only in advanced economies where financial integration is deep enough to transmit demographic pressures through portfolio capital flows. The collapse of KAOPEN interactions on I/Y in the larger panel indicates that the openness-investment channel documented in the companion multilateral paper is not universal.

**Income heterogeneity is proxy-dependent.** The original claim of a "middle-income peak" was based on I/Y, where the demographic effect does decline with income ($Z_1$ from 65.4 in low-income to 16.2 in high-income). But K/Y shows low-income positive ($19.5$, $p < 0.05$), middle-income negative ($-12.7$, $p < 0.01$), and K/L shows a middle-income sign reversal ($-0.15$, $p < 0.01$). No single income story applies across proxies. The most robust finding is that demographics predict I/Y most strongly in low-income economies and the suppression effect is most pronounced in the OECD — a development-stage gradient rather than a middle-income peak.

The finding that demographics drive I/Y but K/Y is marginally negative is consistent with the companion capital deepening paper's results, where $Z_1$ predicts investment-to-GDP ratios ($\beta = 41.1$, $p < 0.001$) but not TFP, while the marginal product of capital responds negatively ($Z_1 = -0.33$, $p < 0.01$). We do not estimate TFP in this paper and therefore treat the "investment without deepening" characterization as a cross-paper inference rather than a standalone finding. The pattern is consistent with investment flowing into maintenance, replacement, and housing rather than productivity-enhancing automation, but confirming this would require decomposing investment by type — an avenue for future work.

**Limitations.** First, I/Y, K/Y, K/L, and labor productivity are all indirect measures of automation. Robot adoption data or task-level automation measures would provide more direct tests of the Acemoglu-Restrepo mechanism. Second, the panel GLS estimator assumes a specific error structure; several specifications produce negative $R^2$ values, indicating poor fit after AR(1) correction. Third, the demographic distance null may reflect measurement limitations (distance from the global mean is a crude proxy for bilateral factor endowment heterogeneity). Fourth, the $Z$ vector captures the full age distribution but may mask within-cohort heterogeneity in labor force participation.

## 6. Conclusion

This paper demonstrates that demographic structure is a significant determinant of investment effort (I/Y) but not of the capital-output ratio (K/Y, which is marginally negative), qualifying the Acemoglu-Restrepo automation hypothesis at the macroeconomic panel level. Aging societies invest a larger share of output, but this does not translate into a higher capital intensity of production. In the current account regression, I/Y acts as a suppressor variable — revealing offsetting investment and consumption channels with $-599\%$ attenuation in the full sample — rather than as a mediator. $Z \times KAOPEN$ interactions on I/Y are insignificant in the expanded panel, indicating that the capital account openness channel is OECD-specific. Demographics are associated with trade openness, but the demographic distance measure is insignificant, limiting claims about demographic comparative advantage.

The investment channel connects to the bilateral rate channel documented in the companion gravity paper, where demographically driven capital flows depress interest rates in recipient economies. The mechanism is potentially self-reinforcing: aging economies generate savings that flow internationally, depressing the cost of capital, though our K/Y marginal negative suggests this does not straightforwardly translate into deeper automation of production.

The eurozone core-periphery asymmetry takes a different form than initially expected: the periphery shows stronger mediation (82% attenuation, with $Z_1$ declining from $-265.8$ to $-47.9$) while the core shows suppression (242% attenuation, with $Z_1$ flipping from $-15.2$ to $+21.5$). Since this operates through I/Y (investment effort) rather than K/Y (production structure), the mechanism is better characterized as a savings-investment imbalance than as a production trap. The policy implication shifts accordingly: the core-periphery divergence reflects asymmetric investment dynamics, not differential automation adoption, suggesting that investment climate reforms in the periphery may be more relevant than industrial policy.

The findings suggest that global aging will reshape investment patterns over the coming decades. However, the TFP null and K/Y marginal negative together warn that higher investment effort does not automatically translate into deeper automation or higher productivity. Understanding the distinction between investment effort and production structure is essential for trade policy, industrial strategy, and international financial architecture.

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